1. Differentiating using First Principals

2. To find the gradient of a tangent at the point A Equation of the tangent takes the form y = mx +c m is the gradient of the tangent

3. 1. Start with a chord of length AB 2. B moves towards A. 3. When B reaches C the chord is getting shorter and closer to A

4. Gradient AB = x f(x) h x+h f(x+h) A B

5. Example: Find the gradient of the tangent at any point x

6. Substituting

7. Example: Find the gradient of the tangent at any point x Multiply out the brackets

8. Example: Find the gradient of the tangent at any point x Divide top and bottom by h

9. Example: Find the gradient of the tangent at any point x h becomes 0

10. Note: Differentiated gives

11. Practice: Differentiate from first principals:

12. Worksheet 1